“God speaks to us through his Word, most certainly. But he also speaks in other ways.”

First, "general revelation is not authoritative or inerrant in the way special revelation is" -- I would counter by saying that both general and special revelation are instances of God revealing himself to mankind, and because it is God who is doing the revealing, by necessity they are both absolutely authoritative and inerrant.  Sin actually impacts our reception of both. By nature we suppress and reject both. If the glory of creation has been impacted by sin, so has the transmission of special revelation. Yet both have been preserved to communicate what God wants us to know about himself.

Second, "rather than quoting the Hebrew Scriptures, which would mean nothing to this audience" -- I think that discounts the supernatural ability of the Scriptures to penetrate the hearts of man. We know that the Holy Spirit reveals the truth of Scripture to people's hearts, whether they are familiar with that scripture or not.  The Bible is self-attesting and thus meaningful.  Paul clearly uses OT revelation in his speech, even if it is not directly quoted (although we don't actually know everything that Paul said - I think it is possible that some of what he said was not recorded). Where else does he come up with "he made from one man every nation of mankind?", a clear reference to Adam. I think he sites those pagan poets to show that they themselves know that what Paul is saying is true, because when God reveals himself, he does so convincingly.

re: general revelation ... GR or NR is limited in what it can communicate about God. While natural revelation communicates enough knowledge about God to condemn man for his sinfulness and rejection of God, it does not communicate redemptive truth.

re:pagan poets ... As I've read through the ancient Greek, Hellenistic, and Roman authors, I am fascinated that they all communicate in their own ways an understanding that man and the universe are deeply flawed due to sin (man's or the gods'). Virgil, for example, writes in his Georgics about a time when human toil, death, and disaster did not exist. However, we now experience these things after Jupiter (i.e. Zeus) murdered his father Saturn (i.e Cronos).

Virgil wrote:

It was Jupiter who put the deadly poison

Into the fangs of serpents; commanded the wolf

To seek and find its prey; ordained that the storm

Should cause the sea to rise and flood the land;

Stripped from the leaves of oaks the dewlike honey

That made them glisten there; hid fire from man;

Turned off the flow of wine that everywhere

Ran in the stream; all this so want should be

The cause of human ingenuity,

And ingenuity the cause of arts...

Natural revelation reveals our sin, but it doesn't reveal our Savior.